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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Loop spaces and the compression theorem


Author: Bert Wiest
Journal: Proc. Amer. Math. Soc. 128 (2000), 3741-3747
MSC (2000): Primary 55P35, 57M27; Secondary 57R25, 55R37
Published electronically: June 7, 2000
MathSciNet review: 1691010
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Abstract:

For a smooth, finite-dimensional manifold $M$ with a submanifold $S$ we study the topology of the straight loop space $\Omega^{st}_SM$, the space of loops whose intersections with $S$ are subject to a certain transversality condition. Our main tool is Rourke and Sanderson's compression theorem. We prove that the homotopy type of the straight loop space of a link in $S^3$ depends only on the number of link components.


References [Enhancements On Off] (What's this?)

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Additional Information

Bert Wiest
Affiliation: CMI, Université de Provence, 39 Rue Joliot Curie, 13453 Marseille cedex 13, France
Email: bertw@gyptis.univ-mrs.fr

DOI: http://dx.doi.org/10.1090/S0002-9939-00-05472-1
PII: S 0002-9939(00)05472-1
Keywords: Compression theorem, straight loop space, rack, quandle, rack space
Received by editor(s): June 18, 1998
Received by editor(s) in revised form: February 19, 1999
Published electronically: June 7, 2000
Additional Notes: The author was supported by a University of Warwick Graduate Award.
Communicated by: Ronald A. Fintushel
Article copyright: © Copyright 2000 American Mathematical Society